BATS Global Markets Inc. is apparently in the final stages of talks to merge with Direct Edge Holdings LLC, a rival stock exchange. That’s according to anonymous sources cited by Jacob Bunge of The Wall Street Journal.

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Merger possible between BATS, Direct Edge

If the merger actually happens, the resulting company would be the second largest stock market operator in the U.S. It would also pose a significant challenge to the NASDAQ and the New York Stock Exchange—the two exchanges which have dominated the U.S. markets for years. The company would use technology specifically aimed at rapid trading.

The sources told The WSJ that the companies could announce a deal in the next few days. However, the talks could still fall through because the deal isn’t done yet.

What would the merged company look like?

Both BATS and Direct Edge each operate two stock exchanges in the U.S. By combining the two companies, the result would be a U.S. stock exchange operator that’s second only to NYSE Euronext (NYSE:NYX). That’s according to the number of shares traded. Data from BATS indicates that the merged company would have about 20.6 percent of the overall market in terms of shares traded.

Of course the Securities and Exchange Commission would still have to approve the merger between the two exchange operators before the deal could happen.

BATS, Direct Edge attempt to grow

Both of the companies have been trying to expand. In March of last year, BATS began an initial public offering, although the company pulled that transaction. A software glitch caused BATS to stop trading its shares. Earlier this month BATS said it wasn’t planning to do an IPO.

Direct Edge had been talking with TMX GROUP INC. (FRA:TXQ) to be acquired by the company. However, the talks broke down about a year ago after TMX was bought by an investment group made up of Canadian banks and financial firms.